Abstract
In this paper, a three-dimensional transient heat conduction equation with an internal source as a thermal flux outflow, decreasing linearly with time from the surface of an elliptic plate is analyzed. Applying theory of integral transformations, the heat conduction model is explained, and its expression is obtained in the form of Mathieu functions. The large deflection of a plate when placed on the elastic foundation is formulated from the potential energy equation neglecting the second strain invariant. A new elegance of modified total strain energy is obtained in these formulations by incorporating the resulting moment and force within the energy term, thus reducing the computation step. The numerical calculations of distribution of the transient temperature, thermal deflection and the maximum normal bending stress are carried out on the outer elliptic boundary and illustrated graphically. Lastly, the corresponding results for circular plates have been presumed when the ellipse degenerates to a circle. The results reveal that the highest tensile stress exists on the major axis of the circular core relative to the elliptical core, which suggests the propagation of low heating due to inadequate heat penetration into the elliptical surface.
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